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I'm assuming you haven't taken any physics courses, so let's start by explaining the concept of a force. Forces are the central focus of classical mechanics. Basically, a force is a push or pull on an object as a result of its interaction with another object. When applied to an object with mass, a force causes the object's velocity to change in some way. ...

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Exponentials come as solutions of this differential equation: dx/dt=c*x where c is a constant and x and t variables. The solution is of the form: x(t)=e^(c*t) A great number of measurements and observations we make can be approximated by this equation. Once the solution is exponential it is logical to take the log since the numbers become large fast ...

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Your question appears to confuse the map for the territory. The scales you mentioned don't occur in nature; they occur in humans' descriptions of nature. Phenomena - actual earthquakes, radiation from stars, etc. in their full complexity are what occur in nature. We often make measurements based on these phenomena and get results such as the total energy ...

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There is the instantaneous force between the mass and the scales, and then there's the reading of the scales. Factors influencing both of these depend on many unknown factors - so here are just some general thoughts. First, if you drop a mass $M$ from height $h$ onto scales with mass $m$, and the two will then move as one, the collision is considered ...

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The obvious solution is to add a "dashpot damper" to the mix so that the equation of motion of the surface is $$y''(t) + 2 \lambda ~ y'(t) + \omega^2 y(t) = -\alpha w_0.$$As usual, in this case the equilibrium comes to a height $y_0 = -\alpha w_0 / \omega^2,$ which reads on the scale as the weight $w_0.$ Substituting $y = y_0 + \eta$ gives a function ...

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At the sensory/neuropsychological level, humans (and probably other creatures) detect and respond on a compressed level versus the actual intensity detected by the eyes, ears, nerve endings, etc. Perceived brightness and loudness changes don't correspond linearly to changes in physical intensity (power/area). Also, sound pitch perception depends on ...

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